Abstract

The second-harmonic dependence on the input fundamental light has been measured in optical fibers having a χ(2) induced by seeding. The results are explained with a model that includes self-phase and cross-phase modulation in the equations governing second-harmonic generation and seeding. This leads to an intensity-dependent phase mismatch whose strength also depends on the relative polarizations of the fundamental and second-harmonic lights. During seeding, the same effects result in a χ(2) grating detuned from exact phase matching.

© 1989 Optical Society of America

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References

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  1. Y. Fujii, B. S. Kawasaki, K. O. Hill, D. C. Johnson, Opt. Lett. 5, 48 (1980).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. U. Osterberg, W. Margulis, IEEE J. Quantum Electron. QE-24, 2127 (1988).
    [CrossRef]
  5. M. E. Fermann, M. C. Farries, P. St. J. Russell, L. Poyntz-Wright, Opt. Lett. 13, 282 (1988).
    [CrossRef] [PubMed]
  6. R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
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    [CrossRef]
  8. H. W. K. Tom, R. H. Stolen, G. D. Aumiller, W. Pleibel, Opt. Lett. 13, 512 (1988).
    [CrossRef] [PubMed]
  9. P. P. Ho, Q. Z. Wang, D. Ji, T. Jimbo, R. R. Alfano, Appl. Phys. Lett. 54, 111 (1989).
    [CrossRef]
  10. M. Arbamowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), p. 297, Eq. 7.1.3.

1989 (1)

P. P. Ho, Q. Z. Wang, D. Ji, T. Jimbo, R. R. Alfano, Appl. Phys. Lett. 54, 111 (1989).
[CrossRef]

1988 (3)

1987 (2)

T. Morioka, M. Saruwatari, Electron. Lett. 23, 1330 (1987).
[CrossRef]

R. H. Stolen, H. W. K. Tom, Opt. Lett. 12, 585 (1987).
[CrossRef] [PubMed]

1986 (1)

1980 (1)

1977 (1)

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Alfano, R. R.

P. P. Ho, Q. Z. Wang, D. Ji, T. Jimbo, R. R. Alfano, Appl. Phys. Lett. 54, 111 (1989).
[CrossRef]

Aumiller, G. D.

Farries, M. C.

Fermann, M. E.

Fujii, Y.

Hellwarth, R. W.

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Hill, K. O.

Ho, P. P.

P. P. Ho, Q. Z. Wang, D. Ji, T. Jimbo, R. R. Alfano, Appl. Phys. Lett. 54, 111 (1989).
[CrossRef]

Ji, D.

P. P. Ho, Q. Z. Wang, D. Ji, T. Jimbo, R. R. Alfano, Appl. Phys. Lett. 54, 111 (1989).
[CrossRef]

Jimbo, T.

P. P. Ho, Q. Z. Wang, D. Ji, T. Jimbo, R. R. Alfano, Appl. Phys. Lett. 54, 111 (1989).
[CrossRef]

Johnson, D. C.

Kawasaki, B. S.

Margulis, W.

U. Osterberg, W. Margulis, IEEE J. Quantum Electron. QE-24, 2127 (1988).
[CrossRef]

U. Osterberg, W. Margulis, Opt. Lett. 11, 516 (1986).
[CrossRef] [PubMed]

Morioka, T.

T. Morioka, M. Saruwatari, Electron. Lett. 23, 1330 (1987).
[CrossRef]

Osterberg, U.

U. Osterberg, W. Margulis, IEEE J. Quantum Electron. QE-24, 2127 (1988).
[CrossRef]

U. Osterberg, W. Margulis, Opt. Lett. 11, 516 (1986).
[CrossRef] [PubMed]

Pleibel, W.

Poyntz-Wright, L.

Russell, P. St. J.

Saruwatari, M.

T. Morioka, M. Saruwatari, Electron. Lett. 23, 1330 (1987).
[CrossRef]

Stolen, R. H.

Tom, H. W. K.

Wang, Q. Z.

P. P. Ho, Q. Z. Wang, D. Ji, T. Jimbo, R. R. Alfano, Appl. Phys. Lett. 54, 111 (1989).
[CrossRef]

Appl. Phys. Lett. (1)

P. P. Ho, Q. Z. Wang, D. Ji, T. Jimbo, R. R. Alfano, Appl. Phys. Lett. 54, 111 (1989).
[CrossRef]

Electron. Lett. (1)

T. Morioka, M. Saruwatari, Electron. Lett. 23, 1330 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

U. Osterberg, W. Margulis, IEEE J. Quantum Electron. QE-24, 2127 (1988).
[CrossRef]

Opt. Lett. (5)

Prog. Quantum Electron. (1)

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Other (1)

M. Arbamowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), p. 297, Eq. 7.1.3.

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Figures (2)

Fig. 1
Fig. 1

Green average power versus IR input average power. The points are experimentally determined values for χ xxx ( 2 ) (upper curve) and χ xyy ( 2 ) (lower curve). The solid curves are the theoretical fits, with a0Lc = 1.5π, Psat = 24 mW, n2s/n2c = 1.58, and χ xxx ( 2 ) / χ xyy ( 2 ) = 6 . 3

Fig. 2
Fig. 2

Green average power versus IR input average power for χ xxx ( 2 ) in a fiber seeded with Q-switched pulses only. The solid curve is the theoretical fit, with a0Lc = −0.82π and Psat = 20 mW.

Equations (10)

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d E 2 d z = i { β E 1 2 exp [ i 2 k ( n 2 ω n ω ) z ] + 4 k n 2 2 σ | E 1 | 2 E 2 } ,
E 1 ( z ) = E 1 ( 0 ) exp ( i n 2 s | E 1 | 2 kz ) ,
I 2 ( L ) = β 0 2 I 1 2 L 2 sin 2 [ ( a 0 L + δ | E 1 | 2 L ) / 2 ] [ ( a 0 L + δ | E 1 | 2 L ) / 2 ] 2 ,
a 0 = [ ( n 2 ω n ω ) 2 k ] k g ,
δ = 2 k ( 2 σ n 2 c n 2 s ) .
I 2 = ( π / 4 ) β 0 2 I 1 2 L c 2 | w ( α L c / 2 ) | 2 ,
α = a 0 + δ | E 1 | 2
k g = 2 k ( n 2 ω n ω ) + 2 k ( 2 σ n 2 c n 2 s ) | E 1 | 2 .
a 0 = 2 k ( 2 σ n 2 c n 2 s ) | E 1 | 2 .
P π L c = 16 . 6 kW cm .

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